SOLUTION: Ten gallons of 30% acid solution is obtained by mixing a 20% solution with a 50% solutions.How much of each solution must be used?

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Question 696133: Ten gallons of 30% acid solution is obtained by mixing a 20% solution with a 50% solutions.How much of each solution must be used?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = gallons of 20% solution needed
Let +b+ = gallons of 50% solution needed
given:
(1) +a+%2B+b+=+10+
(2) +%28+.2a+%2B+.5b+%29+%2F+10+=+.3+
--------------------------
(2) +.2a+%2B+.5b+=+3+
(2) +2a+%2B+5b+=+30+
Multiply both sides of (1) by +2+ and
subtract (1) from (2)
(2) +2a+%2B+5b+=+30+
(1) +-2a+-+2b+=+-20+
+3b+=+10+
+b+=+10%2F3+
and, since
(1) +a+%2B+b+=+10+
(1) +a+%2B+10%2F3+=+10+
(1) +a+=+30%2F3+-+10%2F3+
(1) +a+=+20%2F3+
3 and 1/3 gallons of 20% solution are needed
6 and 2/3 gallons of 50% solution are needed
check answer:
(2) +%28+.2a+%2B+.5b+%29+%2F+10+=+.3+
(2) +%28+%282%2F10%29%2A%2820%2F3%29+%2B+%281%2F2%29%2A%2810%2F3%29+%29+%2F+10+=+3%2F10+
(2) +%28+40%2F30+%2B+10%2F6+%29+%2F+10+=+3%2F10+
(2) +40%2F30+%2B+50%2F30+=+3+
(2) +90%2F30+=+3+
(2) +3+=+3+
OK